Transfering blender to new pc
The least troublesome way to transition from one computer to the next is to copy the contents  of all folders used for your blender projects in the same file structure you had in the old computer.
As you learned already images used as textures are not saved as part of the blend file unless they are packed. But even if the textures are packed, any link or reference to other blend files will be broken if the file does not exist in the specified place.
That is also true for the cache files for physics and other simulations. If the files are not found you will need to bake them again.
Note as well that for video files and image sequences and audio files there is no way to pack them into the file either.
A partial solution is to use relative paths, where the file structure doesn't have to be the exact same, as long as the assets are all all within the same folder as the blend file. But again, all relevant files have to be copied over to other computer.
A different approach would be to remove the drive from the old computer and make it available to the new one as an external drive.
As a last resort, if you don't want to copy all of the files, you can use the old computer as a network drive, through which you can access your files directly without having to copy them over. But the access will be slower.